Printers, copiers, and xerographic machines are machines that produce a pattern on a substrate. Typically they consist of a means of obtaining the desired pattern and a marking engine that fixes the pattern to a substrate. Paper, cloth, and plastic are examples of substrates. A pattern can be fixed to a substrate using ink, pigment, or a similar material. Precise control is required to ensure that the pattern produced by the marking engine is acceptably similar to the desired pattern. Over time, the marking engine can experience unintentional change because its mechanical components can change, the ink can change, and the substrate can change. To compensate for unintentional change, a controller can make intentional changes to the marking process such that the marking engine produces a consistent product.
In performing its function, a controller runs control algorithms and needs control inputs and outputs. An ideal control input for a marking engine controller is the reflectance spectrum of printed materials. A spectrophotometer can be used to produce a reflectance spectrum. An in-line spectrophotometer is a device that can be used for monitoring and control of production processes such as printing and copying. A spectrophotometer that can be used as an in-line spectrophotometer is disclosed in U.S. Pat. No. 6,384,918, which is incorporated herein by reference. Utilized as an in-line sensor, an aspect of the disclosed spectrophotometer produces a measurement, called an in-line spectrum that consists of the reflectance measured at eight different wavelengths. Other types of in-line spectrophotometers can also produce in-line spectrums and those in-line spectrums can have a different number of reflectance measurements made at different wavelengths.
In many applications, a spectrum that includes at least 30 different wavelengths is desired. A well-calibrated and precise spectrophotometer or a similar device, hereinafter called a reference spectrophotometer, can make the desired measurement, hereinafter called a reference spectrum. Reference spectrophotometers typically cannot be used in-line because they tend to be large expensive and slow. A close approximation of a reference spectrum, called a reconstructed spectrum, can be calculated from an in-line spectrum using methods disclosed in U.S. patent application publications numbers 20030050768, 20030055611, and 20030055575. The disclosed methods produce a reconstruction matrix that maps an in-line spectrum to a reconstructed spectrum. The referenced methods use an in-line spectrum and a reference spectrum to produce a reconstruction matrix, but thereafter use in-line spectrums and the reconstruction matrix to produce corrected spectrums.
Current art teaches systems and methods by which a reconstructed spectrum having the quality of a reference spectrum can be produced from an in-line spectrum and a reconstruction matrix when the substrate does not change. In the real world, substrates do change. For example, a specific type of paper used as a printing substrate can change between manufacturing batches. Another example is that two versions of a publication can be printed, one on a high quality paper and the other on a low quality paper. Substrate changes cause the reconstruction matrix to become inaccurate. The reason is because the reflectance spectrum of printed material depends on the reflectance spectrums of both the substrate and the printed pattern and because different types of substrates can have significantly different reflectance spectrums. Prior methods and systems produce excellent results as long as the substrate does not change.
Linear algebra, which includes vector and matrix manipulations, is well known. The prior art and the present embodiment are presented via linear algebraic notation. A few of these notations are of particular interest. One is the diag() function that transforms an M element vector into an M by M matrix with the vector elements on the main diagonal of the matrix. Another is the matrix inverse. A matrix multiplied by its own matrix inverse results in an identity matrix. Another concept is the distance between two vectors. One common measure is the Euclidean distance. Given two vectors with two elements, (a, b) and (c, d), the Euclidean distance is sqrt((a−c)*(a−c)+(b−d)*(b−d)), where sqrt( ) is the square root function. Other distance measures such as the Mahalinobis distance, or absolute difference are also common.
The embodiments described herein therefore overcome the aforementioned limitations and flaws of the prior art.